Number Theory

Problems related to integers, prime numbers, congruences, etc.

Problems in this category

The problem asks to find the hexadecimal equivalent of $X+Y$, where $X = 10010_2$ and $Y = 1111_2$ a...

Number SystemsBinaryHexadecimalBase ConversionArithmetic Operations
2025/3/31

The image presents multiple-choice questions. We will solve questions 34, 35, 36, and 37. Question 3...

Modular ArithmeticModulo Operation
2025/3/31

We are asked to find which of the given numbers cannot be the base of the number $12012$.

Number BasesBase Conversion
2025/3/31

The problem asks us to classify given numbers into different sets of numbers: - N: Natural numbers -...

Number SetsReal NumbersRational NumbersIrrational NumbersIntegersNatural Numbers
2025/3/30

We are given the number 243, which is not a perfect square. We need to find the smallest natural num...

Perfect SquaresPrime FactorizationInteger Properties
2025/3/30

The problem asks us to find the smallest natural number that we need to divide 675 by to obtain a pe...

Prime FactorizationPerfect SquaresDivisibility
2025/3/30

Determine whether the number $\frac{\pi}{5}$ is rational or irrational.

Rational NumbersIrrational NumbersReal NumbersPi
2025/3/21

The problem asks whether the number $7.11$ is rational or irrational.

Rational NumbersIrrational NumbersNumber Representation
2025/3/21

The problem asks to find the smallest natural number that we need to multiply 243 with to make it a ...

Perfect SquaresPrime FactorizationInteger Properties
2025/3/21

We are given the number 675, which is not a perfect square. We need to find the smallest natural num...

Prime FactorizationPerfect SquaresDivisibility
2025/3/21